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I am an undergraduate student in Computer science who has recently developed a very strong interest in logic and computability. I enjoy a lot reading academic papers but I am afraid that my understanding of them might be incomplete or skewed.

This question is similar to: How can I prove my self-studied knowledge? but my unlike the OP I want to specifically test my knowledge of academic papers and I have no one to talk to (other than Mathematics/Mathoverflow)!

There is some graduate courses at my University that are "seminars" where a group of graduate students with a professor discuss a new paper every week. It looks awesome and so interesting... but I am a first-year student and I don't want to come across as arrogant. What to do?

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    A small comment about the seminars: Ask the professor. (Almost) all professors are happy if someone is interested in their field of research. If you worry about coming across as arrogant: As long as you know that your understanding of the subjects might not be perfect and that you are not at the same level as the graduate students there is (almost) no chance that will happen. Just ask the professor polity if you could participate ("passively", i.e., by listening and maybe asking a few questions). If that works out for you then you can ask the professor next term to present a paper by yourself. – The Almighty Bob Jun 12 '15 at 9:20
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Academic papers deal with the state-of-the-art of the field, either pushing it or reviewing it. So, to fully understand them, you need a deep knowledge of the field.

Now, "fully understanding" them might be a bit broad statement. The key of the paper are the problem and the solution, but I put more emphasis on the problem. For, if you are able to understand what the problem is, why is it hard, its background (where it stands in relation to related work) and implications (how future problems are derived from it), you probably have enough subject knowledge to digest the whole paper. The solution is important, but not so much on a fundamental level as on a conceptual, i.e. you don't have to understand every line of a proof to get why a theorem solves a problem.

So, the first step is understanding the problem and the second "getting" the solution. If you want to be more strict with yourself, ask yourself after reading a paper whether you are able to think about the boundaries of the problem or solution, i.e. what could be done to improve them or what could be derived from them (not minding at that point if that is feasible or not).

PS: If you really are doing research in a field, you need to analyze the paper on deeper levels (check the references, the experimental setup, remember the proof from above and the one you read in another paper 3 months ago, etc.), but at your level, the above seems more than enough.

PPS: I don't see a problem with you joining those "seminars". Ask the professor if you could participate in some of them, at the beginning only by being present and listening. See if it suits you. Once you get the hang of it, you can actively be a part of the discussions. It may be hard to keep up, but that shouldn't discourage you. And you shouldn't strive for the level of understanding the graduate students are at, that'll come with time.

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    Many times, the argument in the paper is condensed - not every step is written out for you. Some tests of your understanding include: can you write down all the steps to get from one equation to the next? What assumptions do you have to make to do so? What other assumptions could you make, and how would that change the derivation? – Jon Custer Jun 12 '15 at 19:22
  • I have followed your advice and asked a professor if I could sit in his seminar course. The professor accepted, and is letting me participate to the paper reviews and to the final project requirement. It's awesome, and I am having a blast! :-D Thank you so much – Erwan Aaron Oct 21 '15 at 19:28

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